3 Answers
3

The "dar-" propositions are basically relative propositions. You have some context and then "darüber", "darunter", etc. will give positions relative to the established context. Just like "dieser/diese/dieses" will always refer to an established context. For example:

Der Kopf ist ganz oben. Der Torso befindet sich darunter.

Note the similarity to "dieser":

Der Kopf ist ganz oben. Der Torso befindet sich unter diesem.

The "da(r)-"less prepositions always need the second object (or a substitution like "dieser") to be directly present in the sentence.

Assuming that you are a native English speaker, I recommend digging a little bit deeper into older and more formal forms of English in regards to this construction.

Even today, forms like "thereby" and "thereabouts" are not so uncommon as to be unheard of. Note that just as it was pointed out that there are da/dar, hier, and wo/wor forms, the same holds true for English with there-, here-, and where-. Legal documents are sometimes filled with such constructions.